“HALF-LIFE”
Half-life is the amount of time required for a quantity to fall to half its
value as measured at the beginning of the time period. While the term "halflife" can be used to describe any quantity which follows an exponential
decay, it is most often used within the context of nuclear
physics and nuclear chemistry—that is, the time required, probabilistically,
for half of the unstable, radioactive atoms in a sample to undergo radioactive
decay.
Introduction
The concepts of half life plays a key role in the administration of drugs
into the target, especially in the elimination phase, where half life is used to
determine how quickly a drug decrease in the target after it has been
absorbed in the unit of time (sec, minute, day, etc.) or elimination rate
constant KE (minute-1, hour-1, day-1,etc.). It is important to note that the halflife is varied between different types of reactions. The following section will
go over different type of reaction, as well as how its half-life reaction is
derived. The last section will talk about the application of half-life in the
elimination phase of pharmcokinetics.
Formula for Half-life in Exponential Decay
An exponential decay process can be described by any of the following
three equivalent formulas:
where

N0 is the initial quantity of the substance that will decay (this
quantity may be measured in grams, moles, number of atoms, etc.).

N(t) is the quantity that still remains and has not yet decayed after
a time t.

t1⁄2 is the half-life of the decaying quantity.

is a positive number called the mean lifetime of the decaying
quantity.

is a positive number called the decay constant of the decaying
quantity.
SAMPLE PROBLEMS:
Sample #1:
Ac has a half life of 6.13 hours. How much of a 5.0 mg sample would
remain after one day?
228
Solution:
The first step is to determine the number of half lives that have elapsed:
Number of half lives = 1 half life/6.13 hours x 1 day x 24 hours/day
Number of half lives = 3.9 half lives
For each half life, the total amount of the isotope is reduced by half.
Amount
Amount
Amount
Amount
remaining
remaining
remaining
remaining
=
=
=
=
Original amount x 1/2(number of half lives)
5.0 mg x 2 -(3.9)
5.0 mg x (.067)
0.33 mg
Answer:
After one day, 0.33 mg of a 5.0 mg sample of
228
Ac will remain.
Sample #2:
Iodine-131 has a half-life of 8.040 days. If we start with a 40.0 gram
sample, how much will remain after 24.0 days?
Solution:
24.0 days / 8.040 days = 2.985 half-lives
(1/2)2.985 = 0.1263 (the decimal fraction remaining)
40.0 g x 0.1263 = 5.05 g
Answer:
After one day, 5.05 g sample of Iodine-131 will remain.
My Report in Advanced
Chemistry
“Half-life”
Objectives:
▪To be able to know the half-life of some
radioactive isotopes.
∙To be able to solve the half-life and the
remaining half-life of an isotope.
Submitted to:
Mrs. Eileen Darocca
Teacher
Submitted by:
Angela Taborada
Student
Half-life of some Radioactive Isotopes
Isotopes
Half-life
∙Carbon-14
5730 years
∙Potassium-40
1.26 billion years
∙Thorium-230
75000 years
∙Uranium-238
4.5 billion years
∙Bismuth-212
60.5 seconds
∙Iodine-131
8.07 days
∙Sodium-24
15 hours
∙Polonium-215
0.0018 seconds
∙Radium-226
1600 years
∙Cesium-137
30 years
∙Gold-198
2.69 days
∙Fluorine-20
11.4 seconds
∙Hydrogen-3
12.3 years
∙Lead-210
19.4 years
∙Radon-222
3.82 days
∙Sulfur-35
87.1 days